Introduction to Mathematical Analysis I - Second Edition

6 worked out in detail, and numerous new exercises. In all we added over 50 examples in the main text and 100 exercises (counting parts). We included more prominently the notion of compact set. We defined compactness as what is more commonly termed sequential compactness . Students find this definition easier to absorb than the general one in terms of open covers. Moreover, as the emphasis of the whole text is on sequences, this definition is easier to apply and reinforce. The following are the more significant changes. Chapter 1 Added the proofs of several properties of the real numbers as an ordered field. Chapter 2 We added the proof that compactness is equivalent to closed and bounded in the main text. Chapter 3 We added the theorem on extension of uniformly continuous functions and moved the discussion of Lipschiptz and Hölder continuous functions to the section on uniform continuity. We created a separate section for limit superior/inferior of functions. Chapter 4 We clarified the statement and the proof of the second version of L’Hospital’s rule. We have used these notes several times to teach the one-quarter course Introduction to Mathe- matical Analysis I at Portland State University. As we are now preparing a companion text for the second term (Introduction to Mathematical Analysis II) we now added the roman numeral I to the title.